Distributionally chaotic systems of type 2 and rigidity

In this paper we deal with uniformly rigid systems obtained by a method introduced by Katznelson and Weiss and show that such systems never contain DC2 pairs. On the other hand, we introduce a modification of this technique that leads to a uniformly rigid system with DC2 pairs. We also show that eve...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2017-08, Vol.452 (1), p.659-672
Main Authors: Foryś-Krawiec, Magdalena, Oprocha, Piotr, Štefánková, Marta
Format: Article
Language:English
Subjects:
DC2
Distributional chaos
Hilbert cube
Transitive
Uniformly rigid
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Summary:In this paper we deal with uniformly rigid systems obtained by a method introduced by Katznelson and Weiss and show that such systems never contain DC2 pairs. On the other hand, we introduce a modification of this technique that leads to a uniformly rigid system with DC2 pairs. We also show that every dynamical system contains a pair of distinct points which is not DC2.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.02.056